New Delhi, July 26 -- Calli Brannan, 30, had been working for a grocery deals app for four years when she realized she needed a break.

The start-up had grown since she joined, she was satisfied with what she had accomplished as vice president of customer success, and she was about to plan her wedding. A few weeks of paid time off weren't going to cut it; she needed to step away from her career to regroup.

"It was a bit of a risk but I knew I needed to take this time if I wanted to be able to continue on in corporate or start-ups or start my own business," said Brannan of Royal Oak, Mich. "I was ready for my next step." She is now a little over a month into a sabbatical that she plans to extend into fall.

Brannan isn't alone. Many mille...